I heard it said that the only things Americans know about is World war Two and they don't know that much about that. It's a sobering thought.
To your point, if anyone wants to see the effects of unchecked corporate power, just look at the 19th century and the robber barons. most notably, look at the history of the Pinkerton Detective Agency [1].
"Detective agency" is an inocuous sounding name but at its peak the Pinkertons outnumbered the US Army. Pinkertons were frequently used as striker breakers and to quash any form of labor movement. They did so with the blessing of the US government.
[1]: https://en.wikipedia.org/wiki/Pinkerton_(detective_agency)
While untrammeled corporate power and untrammeled government power are both scary, the effective fusion of the two via state capture is the real nightmare. I think that sort of halfway environment, where there's enough state to be worth capturing but not enough to be an effective counterweight, is the default in a lot of the particularly cursed post-colonial nations - Angola and Burma spring to mind - where traditional means of social organization were sublimated into the colonial state, leaving a vacuum when the colonial state itself began to molder.
Government power is the only thing stopping corporations from exercising violence against you or take away your rights. Look at the way corporations operated in the 19th and early 20th centuries, when they had company towns and private armies coercing votes and killing strikers, or corporations' support for coups and cartels in foreign markets, or just the East India Trading Company, which was a de facto superpower of its time.